Definition:Module/Left and Right Modules
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In the case of a commutative ring, the difference between a left module and a right module is little more than a notational difference. See:
But this is not the case for a ring that is not commutative. From:
it is known that it is not sufficient to simply reverse the scalar multiplication to get a module of the other ‘side’.
to obtain a module of the other ‘side’ it is, in general, also necessary to reverse the product of the ring.
a left module induces a right module and vice-versa if and only if actions are commutative.
- Definition:Left Module
- Definition:Right Module
- Definition:Scalar Ring of Module
- Basic Results about Modules
- Results about modules can be found here.